An edge dislocation inside a semi-infinite plane containing a circular hole

This paper presents an analytical solution of the Green's function for an edge dislocation lying anywhere inside a semi-infinite plane containing a circular hole. The solution is obtained using the Airy stress function method, where the auxiliary function is expressed in series form in the bi-polar coordinate system and the convergence of the solution is ensured by an asymptotic analysis. Stress distributions are presented for different d/R ratios (where d is the distance from the free edge to the centre of the hole of radius R) and various dislocation positions to show the interactive effect of the two boundaries. The Green's function is then employed to model an edge crack growing toward the hole by a continuous distribution of dislocations.